44 
PROFESSOR A. E. 11. LOVE ON THE INTEGRATION OF THE 
is transmitted across the surface, in the sense of the normal (/, wi, n), is, hy 
PoYNTiNcfs Theorem, 
[[— hv) + m (Jin —fw) + n {fv — gu)} c/S ... (98). 
We can, therefore, find tlie rate of dissipation of energy from the condenser, l^y 
forming this integral, for a sphere of large radius, R, and for the functions . . ., 
the normal being drawn outwards. 
If we write, for Imevity, 
X = /R, y = 7nR, ^ = 7;R, K{Gt — R) = i/;. 
the rate of dissipation is 
h (j) h I sill + I) cos .//)' {t- (P + nr) + nr (P + m’) + tp (I- + nr)} rfS 
. . (99), 
taken over the sphere ; and the amount of energy transferred across the sphere in a 
period, !I7 t/(kc), is given l)y the expression"^ 
or it is 
which is 
C'^ /«\ S IT 
47r\2/ 
(kW + t) . . . 
- 27r j" {k^^' cos" 6 + K^rf) sin® 6 dO , 
( 100 ), 
( 101 ). 
Restoring the values of ^ and y, this expression Ijecomes 
( 102 ), 
wliere n is now the order of the spherical harmonic involved in the oscillations. 
When ?’,j — is small compared with Vq, the fraction of the total energy, which is 
dissipated in one period, is obtained by dividing the expression here written by the 
expression (92) ; it is 
^ 7 r( 2 yi + l)(/c/o)®(l + 
-VRo-g)’ ■ 
(103); 
* The exj^ressioii shows that equal amounts of energy are transmitted across the hemisphere in front of 
the aperture and that l»ehind. This arises from the circumstance that the wavedength is of the same order 
of magnitude as the radius of the outer conducting surface, so that the waves bend completely round that 
surface. 
